PHYS2403 Geophysics Simulation Lab

Experiment 1: Gravity Anomaly Forward Modelling (Buried Sphere)

This web simulation visualises the exact gravity anomaly of a buried spherical body. Change depth, radius, and density contrast to see how the profile amplitude and half-width respond under the sphere model.

Model Parameters

Depth z (m)200 m

Depth is measured to the center of the sphere.

Radius R (m)100 m

Gravity scales with the sphere volume, so R matters strongly.

Δρ (kg/m³)+500

Positive contrast gives a positive anomaly; negative contrast gives a negative anomaly.

Presets

Observation mode

The simulation is for observation only. Use the lab manual for the written questions and analysis.

Subsurface Earth Cross-SectionScale: meters

Gravity Anomaly Profile (Δg)mGal vs Distance (m)

Peak Δg: 0.3494 mGal

Half-width: 153.3 m

Factor: z√(2^(2/3) - 1)

Key Physics Equations

Gravity over Buried Sphere

\Delta g(x) = \frac{4}{3}\pi G R^3 \Delta\rho \frac{z}{(x^2 + z^2)^{3/2}} \times 10^5 \text{ mGal}

$G \approx 6.674 \times 10^{-11} \text{ m}^3/(\text{kg}\cdot\text{s}^2)$ is the gravitational constant, $R$ is the sphere radius, $z$ is depth to the center, $\Delta\rho$ is the density contrast, and $x$ is the horizontal distance from the sphere center.

Exact Half-Width Rule

x_{1/2} = z \sqrt{2^{2/3} - 1} \approx 0.76642 z

This represents the exact half-amplitude distance for the buried-sphere profile, allowing the depth to be estimated as: $z = \frac{x_{1/2}}{\sqrt{2^{2/3} - 1}}$ .